My prof in my digital logic design course neglected to explain the implication operation properly and I’m having a hard time understanding what to do in a question on my current assignment. All the references (friends and web) I’ve tried don’t give me a very good explanation with regards to this problem, so here goes…

The question is basically as follows:

a) Show if the implication operation x–>y defined in the table is commutative and associative.

```
x y x-->y
0 0 1
0 1 1
1 0 0
1 1 1
```

Finding the minterm expansion gives the function x’+y, which is obviously commutative given it is an OR function, and I suppose it’s associative as well since there are only two variables, although I’m unsure if there’s anything more to the explanation than just that.

b) Is the operation (x–>y)(y–>x) commutative?

Since (x’+y)(y+x’) = (x’+y) = (y+x’) I assume this operation is commutative.

**Then again, I’m not entirely clear on what x–>y and y–>x are supposed to mean. I guess this is my main problem: I don’t understand the implication function.**

Thanks very much to whoever can help!